Answers : (1)

The greatest integer function of a real number x is represented by [x] or |_x_|.

For all real numbers x, the greatest integer function returns the largest integer less than or equal to x.

In other words, the greatest integer function rounds down a real number to the nearest integer.

More about Greatest Integer Function

Greatest integer functions are piece-wise defined.

The domain of the greatest integer function is the set of real numbers which is divided into a number of intervals like [-4, 3), [-3, 2), [-2, 1), [-1, 0), [0, 1), [1, 2), [2, 3), [3, 4) and so on.

Hint: [a, b) is just an interval notation which means a ≤x< b, where x is a real number in the interval [a, b).

When the interval is of the form [n, n + 1), where n is an integer, the value of the greatest integer function is n. For example, the value of the greatest integer function is 4 in the interval [4, 3).

The graph of a greatest integer function is not continuous. For example, the following is the graph of the greatest integer function f (x) = |_x_|.

All the best.

AKASH GOYAL

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